Question: Which of the following numbers is a factor of 64? ${3,4,5,6,9}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $64$ by each of our answer choices. $64 \div 3 = 21\text{ R }1$ $64 \div 4 = 16$ $64 \div 5 = 12\text{ R }4$ $64 \div 6 = 10\text{ R }4$ $64 \div 9 = 7\text{ R }1$ The only answer choice that divides into $64$ with no remainder is $4$ $ 16$ $4$ $64$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $64$ $64 = 2\times2\times2\times2\times2\times2 4 = 2\times2$ Therefore the only factor of $64$ out of our choices is $4$. We can say that $64$ is divisible by $4$.